Abstract
Bi-criteria lexicographical minimization problems with the makespan as the primary objective and the total machine assignment costs as the secondary objective have been recently introduced to the scheduling research, and polynomial time (r+1,1)-approximation algorithms have been suggested for their solution, where 1<r<2 is the performance ratio of an approximation algorithm for P||Cmax. We improve these results by presenting a polynomial time (1.5r−1,1)-approximation algorithm for the additive cost type. Then, we introduce a problem of minimizing the total machine assignment cost over the Δ-approximate solutions of the makespan minimization problem. We prove that this new problem is strongly NP-hard and pseudo-polynomially non-approximable in general. A polynomial time approximation algorithm with a guaranteed approximation ratio is presented for the additive cost type and bounded ratio between the maximal and minimal machine costs. An O(mn2k) time dynamic programming algorithm is also presented, where k is the fixed number of distinct job processing times.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.